In the previous two DDT validation cases, transition to detonation occurred in a confined environment due to detonation tube walls. During rocket engine testing however, the principal scenario in which a DDT event might occur would be in an unconfined or semi-confined environment due to external ignition of a vapor cloud. For example, Figure 34 depicts a typical external ignition of the RS-25 engine during testing at the SSC A-1 test stand. While a
detonation did not occur during this event, a substantial overpressure did result from external ignition of a hydrogen vapor cloud, as indicated by the spherical luminous flame surrounding the nozzle exit region. The hydrogen vapor cloud formed outside the rocket nozzle due to the engine’s designed operation of leading the flow of hydrogen relative to oxygen during engine start. The excess hydrogen was pushed through the combustion chamber and nozzle but was delayed in combusting due to fuel-rich ignition limits. Retractable H2-Air torch igniters were present on the test stand to propel a turbulent flame-jet into the engine’s exhaust and thereby consume the hydrogen vapor cloud as it mixed with the surrounding air. In order to minimize the strength of any overpressure event, the igniters were placed as close to the nozzle exit as possible.
It is certainly feasible under liquid rocket engine testing environments that a scenario might occur in which the hydrogen vapor cloud deflagration accelerates into a detonation should proper conditions exist. Since the majority of our safety devices on the test stands involve small H2-Air torches to burn off excess hydrogen, it was pertinent to investigate the existence of suitable validation data similar cases. Ideally, the validation data set would require conditions in which DDT events did not occur to ensure the model did not erroneously predict a detonation. In addition, since rocket propulsion test applications involve a range of H2-O2-N2 mixtures rather than H2-Air, it was desirable for the data set to consist of H2-O2 propellants with varying amounts of nitrogen.
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Figure 34: RS-25 Engine External Ignition at the SSC A-1 Test Stand
Experiments have indicated that detonation initiation using a flame-jet depends on the relative size of the jet (diameter) to the detonation cell-width. Numerous authors have proposed a general linear correlation between jet diameter and cell-width. Figure 35 is a summary chart reproduced from Ref. [37] depicting the relationship between these geometrical and chemical parameters for a H2-O2-N2 system. Open symbols represent test conditions in which the flame failed to transition to detonation, while the closed symbols correspond to conditions in which DDT eventually occurred in the system. In this figure, the relationship of 14 times cell-width and 24 times the cell-width were plotted for reference. While, there does not appear to be a
consistent linear relationship that covers the full range of flame-jet diameters tested by these two researchers, the data does suggest a rough order-of-magnitude criterion of d/ > 24 might be used with caution for engineering-design purposes.
Figure 35: Assumed Linear Correlation for Flame-Jet Initiation of H2-O2-N2 Spherical Detonations
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The use of detonation cell-width as a correlation parameter stems from historical roots of fundamental detonation research. Since cell-width is an empirically determined quantity rather than a primary system parameter, its use in the correlation is not intuitive for general
engineering applications. Furthermore, cell-width does not really identify the mechanism altering the DDT event as several factors can change the measured cell-width. Some of these factors include equivalence ratio, initial pressure/temperature, and diluent concentrations. For the current application of rocket testing, the primary parameter that would affect the detonation cell- width would be the amount of nitrogen dilution. Specifically, nitrogen dilution alters the acoustic wave speeds and combustion dynamics in such a way that it has a first-order effect on the flame acceleration, DDT and subsequent transverse waves that sustain propagating detonation
waves. This sensitivity to nitrogen dilution is thereby exhibited experimentally in the form of changes to the measurable cell-width.
Pfahl and Shepherd conducted their flame-jet initiation experiments in the CALTECH HYJET facility depicted in Figure 36 [38]. This system consisted of a small driver vessel (28 liters) connected to a substantially larger receiver vessel (1180 liters). A diaphragm initially isolated the gas mixtures in the vessels. Inside the driver vessel, deflagration was initiated via spark, which sent combustion gases through a jet nozzle, ruptured the diaphragm, and established a combusting jet flow into the receiver vessel. The experimental facility allowed for adjustments in both the flame-jet size and the mixture conditions in the receiver vessel. Since the volume of the receiver vessel was substantially larger than the flame-jet size, this configuration mimics an “open” environment for DDT to occur. In their study, they proposed a nitrogen/jet-diameter correlation for flame-jet initiation of detonations. Figure 37 shows their data for stoichiometric H2-O2 systems at 1 bar and 295K with various amounts of nitrogen dilution. This is a subset of the same data that was presented earlier in Figure 35, but now provides a more descriptive correlation than that of “cell-width”. The value in Figure 37, which replaced the cell-width parameter, is the molar fraction of nitrogen to oxygen as indicated by the stoichiometric chemical equation in Figure 37. Using this correlation, the researchers identified three
combustion regimes for flame-jet diameters less than 100 mm. The three possible regimes were deflagration, secondary explosion resulting in DDT, and prompt initiation of detonation. For reference, the current author has superimposed a curve representing D/ ~ 20 on the figure. While this curve closely matches the prompt initiation/DDT boundary, a linear relationship for the DDT/deflagration boundary does not exist. Since this boundary is more relevant for safety concerns, this data set provides a good source for CFD model validation. The Pfahl and
Shepherd data is also well suited for geometrical sizes of interest in rocket propulsion testing, as the exit torches used at SSC are on the order of 2 to 3 inches (25-76 mm) in diameter. The Dorofeev data [39] shown in Figure 35 was also used as validation data for large flame-jet diameter cases.
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Figure 36: Schematic of the CALTECH HYJET Facility [Ref. 38]
Figure 37: HYJET Facility Data Depicting the Non-Linear Dependency of the Flame-Jet Initiation of H2-O2-N2 Spherical Detonations [Ref. 38]
B. CFD Model
An axisymmetric structured mesh was used to simulate the flame-jet injection into the receiver vessel as depicted in Figure 38. The CFD mesh resolution used in the flame-jet initiation cases was a uniform spacing of 2 mm. Rather than model the entire volume of the
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driver and receiver vessels, the driver flow was approximated with a constant mass flow rate of combustion gases as estimated in the experiments. Since the time scales associated with the driver blow-down are much longer than time scales required for establishing the combustion mode in the receiver vessel, the assumption of a constant mass flow inlet was reasonable. Also, the diaphragm rupture, which occurred in the experiments, was mimicked in the CFD model by an instantaneous mass inflow boundary at simulation start. These inflow conditions are
summarized in Figure 38. A spark ignition source was not required as the flame-jet provided the means for deflagration initiation in the receiver vessel. The Shang 7s/7r mechanism was used in this study.
A subsection of the receiver vessel was modeled by utilizing supersonic extrapolation conditions for the exit boundaries. The domain size for the receiver region was selected such that the largest flame-jet (Dorofeev, 400 mm) with the longest time to reach a steady
combustion state (deflagration, =3.76) could be fully captured. For the largest flame-jet condition of 400 mm, this corresponded to placing the exit boundaries an axial and radial
distance of 10 and 5 jet diameters away from the nozzle exit, respectively. Therefore, smaller jet sizes and/or less nitrogen dilution test cases would have no issue of reaching their final
combustion mode within the CFD domain limits. This approach was done to minimize the computational resources required for the study. Lastly, no significant changes were required to the solver settings for modeling the flame-jet initiation cases.
Figure 38: CFD Mesh Topology and Inflow Conditions for Flame-Jet Initiation Studies
C. Results
The smaller jet configuration of 64 mm was modeled with a nitrogen-to-oxygen molar fraction of 1.2. The experimental data of Phafl and Shepherd indicated that this configuration resulted in prompt initiation of detonation within the receiver vessel. Figure 39 provides the predicted density gradients and Mach number contours for this scenario. The CFD results show that the model also predicted prompt initiation as the flame-jet exhausted into the receiver vessel. A hemispherical detonation wave was generated within 5 msec of flow initiation. The Mach number distributions confirm that the combustion is sonic (M=1) relative to the combustion sound speed directly behind the leading shock front.
The simulation was then repeated using the same mesh but with a =2.0 mixture. This test configuration corresponded to just within the DDT regime of the experimental data set. Figure 40 depicts that DDT was in fact predicted to occur at approximately 10.5 msec after flame-jet injection. This is substantially later in time than the previously modeled test condition with less nitrogen dilution. The DDT in this case was observed to occur on the periphery of the jet as the
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flame front expanded. The mechanism for flame acceleration appeared to be due to the well- known Darrieus-Landau (DL) instability exhibited by expanding flame fronts. The DL instability is manifested in the form of corrugated or wrinkled flame fronts due to hydrodynamic instabilities of thin premixed flame fronts undergoing thermal expansion. Along the surface of the flame front, instabilities of relatively small wavelength grow fast causing the “cellular” like deformation with multiple shear-layers being produced in its wake. The flame wrinkling produces local
acceleration and under certain circumstances localized explosions in the premixed system. Simulations of the larger jet diameter case of 400 mm were then conducted. Data was only available from Dorofeev for the case of H2-Air (=3.76). The simulation results are shown in Figure 41, and they confirm the experimental observation that DDT was not generated under these conditions. Figure 41 also depicts that while the DL instability was present in the expanding flame front, the conditions were such that the flame could not accelerate rapidly enough to produce a detonation. This was not the case when the nitrogen dilution was reduced to =2.0. By reducing the amount of nitrogen dilution, the DL instability was capable of
accelerating the flame to the point in which micro-explosions occurred. Figure 42 shows that at 8.5 msec, density waves had started to accumulate ahead of the flame front. This pressure build-up resulted in continuous acceleration of the flame as indicated by the increasing value in Mach number ahead of the flame front. A localized explosion was eventually produced at 9.5 msec in the jet core. As was seen in the smaller flame-jet of Figure 40, localized explosions also occurred along the flame front well away from the periphery of the jet.
Lastly, the larger jet configuration was simulated with no nitrogen dilution (=0). These results, provided in Figure 43, confirm the expected prompt-initiation of the detonation wave via the flame-jet. Therefore, while the Dorofeev data does not explicitly delineate the three
combustion regimes based on nitrogen dilution, the predicted behavior was consistent with that of the smaller jet data of Phafl and Shepherd.
Two important conclusions can be drawn from the simulation results. First, combustion modes (prompt detonation, DDT, deflagration) were accurately predicted for flame jet initiation of H2-O2 mixtures with varying amounts of nitrogen dilution. This was a critical demonstration that detonation predictions in these environments could be made. However, just as importantly, the modeling approach did not produce erroneous predictions of a detonation when the
necessary flame acceleration were not sustainable. The second important conclusion was that the flame-jet initiation models could be conducted with an axisymmetric model. For the cases simulated, it was not necessary to capture three dimensional jet dynamics and their interaction with the flame development. However, this may not be the case for all axisymmetric flame-jets. Also, three-dimensional models would have to be used for non-circular jets, jets with cross-flow or where buoyancy forces begin to play a significant role.
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